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Math Help - taylor expansion

  1. #1
    tur
    tur is offline
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    taylor expansion

    Hi to all,

    I'm trying to find a general formula for the taylor expansion around 0 of

    ln(cos(x))

    I know how to get the first terms yet no general formula for the series that i get

    does anyone know how to do it?

    Thanks, Lior
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  2. #2
    MHF Contributor
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    Quote Originally Posted by tur View Post
    Hi to all,

    I'm trying to find a general formula for the taylor expansion around 0 of

    ln(cos(x))

    I know how to get the first terms yet no general formula for the series that i get

    does anyone know how to do it?

    Thanks, Lior
    If you start with the Taylor series for \tan x

    \sum_{n=1}^{\infty}B_{2n} \frac{(-4)^n \left( 1 - 4^n\right)}{(2n)!}\, x^{2n-1} where B_{2n} are the Bernoulli numbers (see Taylor series - Wikipedia, the free encyclopedia)

    then you can integrate term by term.
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  3. #3
    tur
    tur is offline
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    thanks

    Thanks a lot.

    Lior
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